This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A321903 #14 Feb 09 2020 02:42:43
%S A321903 1,1,3,1,3,5,7,1,3,13,7,9,11,5,15,1,19,29,7,25,27,21,15,17,3,13,23,9,
%T A321903 11,5,31,1,51,61,7,57,59,53,15,49,3,45,23,41,11,37,31,33,19,29,39,25,
%U A321903 27,21,47,17,35,13,55,9,43,5,63
%N A321903 Irregular table read by rows: T(n,k) = (2*k+1)^(-1/(2*k+1)) mod 2^n, 0 <= k <= 2^(n-1) - 1.
%C A321903 T(n,k) is the unique x in {1, 3, 5, ..., 2^n - 1} such that x^(-(2*k+1)) == 2*k + 1 (mod 2^n).
%C A321903 The n-th row contains 2^(n-1) numbers, and is a permutation of the odd numbers below 2^n.
%C A321903 For all n, k we have v(T(n,k)-1, 2) = v(k, 2) + 1 and v(T(n,k)+1, 2) = v(k+1, 2) + 1, where v(k, 2) = A007814(k) is the 2-adic valuation of k.
%C A321903 For n >= 3, T(n,k) = 2*k + 1 iff k == -1 (mod 2^floor((n-1)/2)) or k = 0 or k = 2^(n-2).
%C A321903 T(n,k) is the multiplicative inverse of A321902(n,k) modulo 2^n.
%F A321903 T(n,k) = 2^n - A321902(n,2^(n-1)-1-k).
%e A321903 Table starts
%e A321903 1,
%e A321903 1, 3,
%e A321903 1, 3, 5, 7,
%e A321903 1, 3, 13, 7, 9, 11, 5, 15,
%e A321903 1, 19, 29, 7, 25, 27, 21, 15, 17, 3, 13, 23, 9, 11, 5, 31,
%e A321903 1, 51, 61, 7, 57, 59, 53, 15, 49, 3, 45, 23, 41, 11, 37, 31, 33, 19, 29, 39, 25, 27, 21, 47, 17, 35, 13, 55, 9, 43, 5, 63,
%e A321903 ...
%o A321903 (PARI) T(n, k) = my(m=1); while(Mod(m, 2^n)^(-(2*k+1))!=2*k+1, m+=2); m
%o A321903 tabf(nn) = for(n=1, nn, for(k=0, 2^(n-1)-1, print1(T(n, k), ", ")); print)
%Y A321903 Cf. A007814.
%Y A321903 {x^x} and its inverse: A320561 & A320562.
%Y A321903 {x^(-x)} and its inverse: A321901 & A321904.
%Y A321903 {x^(1/x)} and its inverse: A321902 & A321905.
%Y A321903 {x^(-1/x)} and its inverse: this sequence & A321906.
%K A321903 nonn,tabf
%O A321903 1,3
%A A321903 _Jianing Song_, Nov 21 2018